Chapter 13, Problem 49A

Which requires more fuel—a rocket going from Earth to the moon, or a rocket coming from the moon to Earth? Why?

To determine

To identify: Whether a rocket going from Earth to Moon or coming from Moon to Earth requires more fuel.

Answer to Problem 49A

Rocket require more fuel to move from earth to moon than the rocket move from moon to earth.

Explanation of Solution

Introduction:

There are four fundamental forces in the universe namely gravitational force, weak force, strong force, and electromagnetic force. Every object in the universe is influenced by the above one or more forces. Force acting on the every massive object due to other body is due to the gravitational force.

When rocket is projected in space, it is acted upon by the force due to the gravity in downward direction. Upward movement of rocket requires grater force against the gravity. The force acting on the rocket is shown in following figure.

Net upward force of rocket is,

  $\begin{array}{l}F=F_T-F_W\\ F=F_T-Mg\left(1\right)\end{array}$

Where,

F_Tis thethrust force

F_Wis the force due to weight of rocket.

Thrust force is exerted by the burning of propellant on the rocket which produces exhaust gases. When rocket launch from Earth, according to equation (1) thrust force require to overcome the weight force of the rocket. Since the mass of the rocket is same on Earth and Moon. Value of g on earth is 9.8 m/s². Similarly, when rocket launch from the surface of the moon, thrust force require overcoming the weight force of the rocket on Moon. Value of g on Moon is 1.625 m/s². The force due to weight of the rocket on the surface of the Earth is greater as compared to force due to weight of the rocket on the surface of the Moon. In order to move rocket in upward direction, it requires more thrust force on the surface of Earth than the Moon. For more thrust, more exhaust gases has to propel out through rocket which require more fuel.

Conclusion:

Therefore, due to the large value of acceleration due to gravity on the Earth than Moon, rocket require more fuel to move from Earth to Moon.